Part 2: Amplitude

1. Pluck the string gently and consider the sound it makes. If you were to plot the amplitude of the string sound over time, what shape would you expect the plot to have? Now, pluck the string more forcefully.

   Ensure that the waveform is not clipping. Clipping occurs if the amplitude is too large to be recorded properly. This is evidenced by the pluck recording being cut off, clipped, or limited at the boundaries of the waveform display (in this case -1 and 1 on the vertical axis). If clipping is occurring, reduce the input gain (volume) slightly for the sound interface. This can often be accomplished by turning a knob on the sound interface. Sometimes it is necessary to adjust the volume in software with a control panel. Continue after you have ensured that clipping is not occurring.

   Does the string sound differently when plucked more forcefully? How would the shape of the plot differ from the shape of the gentle pluck plot?

   Record your expectations below:
   

2. If pd is receiving audio signals as confirmed by Part 1, you are ready to make your first measurement of a string pluck. Press the button marked ``Click Here to Begin Recording 1''. Recording begins immediately even though the recording display does not immediately update. Pluck the string gently and wait. After 10 seconds have elapsed, the plot marked ``recording1'' will update with the recorded waveform. Clicking the record button again will overwrite a previous recording.

   Think about how the string looks when it is vibrating. It is vibrating so fast that you probably cannot track it moving back and forth with your eyes, you merely see a blur. This blurring also affects the waveform display. In 10 seconds, the string vibrates so many times that no visual representation can trace out all of the individual cycles. As a result, the waveform display shows only the outline of the string's vibrations-much like how you can see the edges of the blurring action when you watch the vibrating string with your eye.

3. Next, make a recording of a harder string pluck. Using the same procedure, click the button marked ``Click Here to Begin Recording 2'' and then pluck the string firmly.

   You should now have a graphical display of the two waveforms similar to the display in Figure 3. Note the difference in the two recorded waveforms. The recorded samples can be played back by clicking the appropriate ``Click Here to Play Recording'' button. Do they differ in any ways besides volume?

   Figure 3: Screen-shot of pd patch 1-1, showing recorded string envelopes.

   

4. Note that while the string plucks decay over time, the decays are not perfectly exponential. This is because vibrating strings are more complex than lightly-damped oscillators. However, the beginnings of the decays should at least be approximately exponential. Consider what the sources of friction with respect to the two plucks are. How should the initial decay rates of the two recordings compare?

   In a moment, you will determine the time constants for your recordings. Scroll down to the bottom of the Pd patch window. You should see two plots called log(recording1) and log(recording2). They correspond to $10\log _{10}E(t)$ for the gentle and hard string plucks, respectively. Note that they do not make out perfect lines. However, they should be comparable to Figure 4, where the red lines indicate the way that a line may be fit approximately to the beginnings of the plucks. The time constants for these recordings are about 0.8sec and 1sec.

   Figure 4: Log-total energies $10\log _{10}E(t)$ for a gentle pluck (above) and a harder pluck (below).

   
   Now calculate the time constants for your recordings. If you wish to check your method, you may use the given time constants for Figure 4. How do your time constants compare? How should they compare?

   Record your answers below: